Abstract
Transport of momentum in slow flows of concentrated suspensions may be strongly dependent upon the fluctuations of particles about their mean motion. The intensity of the velocity fluctuations is an internal field that is the analog of temperature in classical kinetic theories. This viscous temperature is governed by a balance law that includes flux, production, and dissipation terms. We provide heuristic arguments to motivate the forms of the viscosity, conductivity, dissipation, and pressure in a theory that includes the viscous temperature. The approach parallels previous developments for dry, granular materials. Phenomena observed in flows of concentrated suspensions, including apparent normal stresses and shear-induced diffusion, are contained within the structure of this theory.
Partially supported by the U. S. Army Research Office through the Mathematical Sciences Institute at Cornell University.
Supported by the U. S. Department of Energy under contract DE-AC04-76DP00789 to Sandia National Laboratories.
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Jenkins, J.T., McTigue, D.F. (1990). Transport Processes in Concentrated Suspensions: The Role of Particle Fluctuations. In: Joseph, D.D., Schaeffer, D.G. (eds) Two Phase Flows and Waves. The IMA Volumes in Mathematics and Its Applications, vol 26. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9022-0_5
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DOI: https://doi.org/10.1007/978-1-4613-9022-0_5
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